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Torres de Hanói de 3 e 4 pinos: abordagens para o Ensino Básico

2020; Sociedade Brasileira de Matemática; Volume: 8; Issue: 05 Linguagem: Inglês

10.21711/2319023x2020/pmo842

2319-023X

Débora Borges Ferreira, Edvan Pontes de Oliveira, Francisco Quaranta Neto,

Physical Education and Gymnastics

In this work we show how to explore mathematical concepts using the classical puzzle Tower of Hanói with 3 pegs, and how to find the solution for one of the variations with 4 pegs.For the classical case with 3 pegs, we investigated a mathematical formula that express the minimum amount of moves required to win the game based on the number of disks, we use recurrences, mathematical modeling and geometric progressions.We also present formulas for the number of times a disc occupies each one of the pegs during the ideal puzzle solution, that is, the one that uses the least amount of moves possible.For the variation with 4 pegs, known Reve´s puzzle, we find a closed formulae that express the minimum quantity of moves to win the game.